A time-dependent approach to the study of atomic autoionization in two-electron systems is formulated. In the first step a two-dimensional (2D) model He atom is constructed by replacing the full 3D electrostatic interaction with a 1D soft-core interaction. The autoionization decay of doubly excited states constructed within the model is calculated by both standard perturbation theory and direct solution of the time-dependent Schrödinger equation. Configuration-interaction theory is invoked to obtain correlated resonance states, and strong laser fields are found to alter the decay rates. In the second step the full 6D wave function for the He atom is expanded in coupled spherical harmonics using a procedure as described by C. Bottcher, D. R. Schultz, and D. H. Madison [Phys. Rev. A 49, 1714 (1994)]. Solution of the time-dependent Schrödinger equation reduces to solving the propagator equations for the 3D expansion coefficients on a B-spline collocation lattice. Autoionizing decay rate calculations using product resonance states are found to be in qualitative agreement with the 2D model results.